Verifying conservative field

Homework Statement

Verify the following force field is conservative.
F = 2xcos2yi - (x2+1)sin2yj

Homework Equations

∇xF=0

The Attempt at a Solution

I'm pretty sure this is just a mistake in the book, but according to my calculations, this isn't a conservative force.
I used the determinant method to do the curl of F to find -2xsin(2y) + 4xsinycosy. Unless those two terms cancel each other to equal 0, then the force isn't conservative and there's a mistake in the book.